Free tool · Production and quality
Process Capability Calculator (Cp, Cpk, Pp, Ppk)
Work out Cp, Cpk, Pp and Ppk from your specification limits and measurements, and check them against 1.33 and 1.67
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Specification limits
· from the drawing or customer specProcess data
Good to know
- Cp and Pp compare the width of the tolerance with the width of the process (6 sigma). They ignore where the process is centred.
- Cpk and Ppk use the distance from the mean to the nearer limit, so an off-centre process scores lower.
- Cp and Cpk use short-term (within) variation. Pp and Ppk use all the variation, including drift and shifts between batches. A big gap between them means the process moves over time.
- The indices assume the process is stable and the readings follow a normal curve. Check a control chart first.
- NIST suggests at least about 50 readings for a reliable index; small samples give a wide margin of error.
Results
Ppk
1.26
Nearer the upper limit: mean 12.0118, mid-point of the spec 12
Overall performance
Pp
1.78
Ppk
1.26
Below 1.33: substandard under the AIAG PPAP default. Expect a corrective action plan and more inspection until it improves.
Overall σ = 0.00749 (sample standard deviation, n − 1)
Upper Ppu = 1.26, lower Ppl = 2.31. Expected out of spec if normal: 83 ppm.
Within (short-term) capability
Cp
3.67
Cpk
2.58
At or above 1.33: meets the usual default for ongoing production.
Within σ = 0.00364 (average moving range 0.0041 ÷ 1.128)
Upper Cpu = 2.58, lower Cpl = 4.75. Expected out of spec if normal: under 1 ppm.
Working (Ppk)
Pp = (USL − LSL) ÷ 6σ = 0.08 ÷ (6 × 0.00749) = 1.78
upper = (USL − x̄) ÷ 3σ = 0.0282 ÷ 0.02247 = 1.26
lower = (x̄ − LSL) ÷ 3σ = 0.0518 ÷ 0.02247 = 2.31
Ppk = smaller of the two = 1.26
Thresholds are the AIAG PPAP manual's defaults, used when the customer sets none. Many customers ask for more, such as 1.67 Ppk at approval and 1.33 Cpk in production, or 2.0 for safety characteristics. Your customer's requirements apply first.
How it works
What this tool does.
Calculate process capability indices Cp, Cpk, Pp and Ppk from the upper and lower specification limits and either a mean and standard deviation or a list of measurements. Within sigma comes from the average moving range, overall sigma from the sample standard deviation, with the AIAG PPAP thresholds explained.
Enter the upper and lower specification limits from the drawing. Then either paste your measurements in the order the parts were made, or type a mean and a standard deviation and say whether it is the overall or the within figure. From pasted data, the calculator works out the mean, the overall standard deviation (dividing by n − 1) for Pp and Ppk, and the within standard deviation for Cp and Cpk as the average moving range of consecutive readings ÷ 1.128. It shows each index, the upper and lower one-sided values, the expected parts per million outside the limits if the data are normal, and a verdict against the AIAG PPAP defaults. It warns when you have few readings or readings already outside the limits.
Rules and dates last reviewed: October 2026
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: 6.1.6 What is process capability?
- NIST/SEMATECH e-Handbook of Statistical Methods: 6.3.2.2 Individuals control charts (d2 = 1.128)
- Steiner, Abraham and MacKay, University of Waterloo: Understanding Process Capability Indices (quotes the AIAG PPAP and QS-9000 thresholds)
- Kongsberg Automotive: Supplier Quality Manual, March 2023 (1.67 Ppk initial, 1.33 Cpk ongoing, 2.0 for safety characteristics)
Process Capability Calculator (Cp, Cpk, Pp, Ppk) formula
Cp = (USL − LSL) ÷ 6σ within. Cpk = min(USL − x̄, x̄ − LSL) ÷ 3σ within. Pp = (USL − LSL) ÷ 6s. Ppk = min(USL − x̄, x̄ − LSL) ÷ 3s. Here x̄ is the mean, s is the overall sample standard deviation (n − 1), and σ within = average moving range ÷ d2, with d2 = 1.128 for ranges of two consecutive readings.
Worked example
A CNC shop in Pune turns bushes with a bore of 12.00 ± 0.04 mm, so USL = 12.04 mm and LSL = 11.96 mm. For a customer’s PPAP it measures 30 parts in a row. The readings have a mean of 12.0118 mm, a sample standard deviation of 0.00749 mm and an average moving range of 0.004103 mm. The bore creeps up through the run as the tool wears.
- σ within = 0.004103 ÷ 1.128 = 0.003637 mm
- Cp = 0.08 ÷ (6 × 0.003637) = 0.08 ÷ 0.021822 = 3.67
- Cpk = min(12.04 − 12.0118, 12.0118 − 11.96) ÷ (3 × 0.003637) = 0.0282 ÷ 0.010911 = 2.58
- Pp = 0.08 ÷ (6 × 0.00749) = 0.08 ÷ 0.04494 = 1.78
- Ppk = 0.0282 ÷ (3 × 0.00749) = 0.0282 ÷ 0.02247 = 1.26
Part to part, the process is very capable (Cpk 2.58). But the drift from tool wear spreads the whole run, and the mean sits nearer the upper limit, so Ppk is 1.26, below the AIAG PPAP default of 1.33. The shop should centre the bore lower and change or offset the tool more often, then repeat the study.
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Questions
Process Capability Calculator (Cp, Cpk, Pp, Ppk), answered.
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What is the difference between Cp and Cpk?
Cp compares the width of the tolerance with the spread of the process (6 sigma). It does not care where the process is centred. Cpk uses the distance from the mean to the nearer limit, so it falls when the process is off-centre. If the process sits exactly in the middle of the tolerance, Cp and Cpk are equal.
What is the difference between Cpk and Ppk?
They use different standard deviations. Cpk uses short-term, within variation, estimated from ranges of readings taken close together (average moving range ÷ 1.128 for individual readings). Ppk uses the overall sample standard deviation of all readings, which also includes drift and shifts over time. A Ppk much lower than Cpk means the process moves between batches, shifts or tool changes.
What Cpk or Ppk value is acceptable?
The AIAG PPAP manual’s default for an initial study is: above 1.67 meets the criteria; 1.33 to 1.67 may be accepted with extra attention until an ongoing Cpk of 1.33 is shown; below 1.33 is substandard and needs a corrective action plan and more inspection. Customers can set their own figures. Many supplier quality manuals ask for 1.67 Ppk at approval and 1.33 Cpk in production, and 2.0 for safety characteristics.
How is the within standard deviation worked out from individual readings?
Take the absolute difference between each reading and the one before it (the moving ranges), average them, and divide by d2 = 1.128, the constant for ranges of two. NIST uses the same estimate for individuals control charts. For readings taken in subgroups, the average subgroup range is divided by the d2 for that subgroup size instead.
How many readings do I need for a capability study?
More is better. NIST notes that most capability estimates are valid only when the sample is large enough, which is generally thought to be about 50 independent values. Your customer may ask for more. With 30 readings, as in the example above, treat the result as a first look.
Do process capability indices need normal data?
Yes. Cp, Cpk, Pp and Ppk assume the readings follow a normal curve and the process is stable. If the data are skewed, NIST suggests transforming them, for example with a Box-Cox transformation, or using percentile-based indices. Check a control chart first: an index from an unstable process does not predict future output.
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